TIJUANA, Mexico —As President Trump battles with Congress over a giant wall to block immigrants, a lesser-known policy could soon take effect that might have a far deeper impact along the U.S.-Mexican border.

In a major change, the Trump administration plans to start requiring migrants to remain in Mexico while their asylum cases crawl through American courts, a process that is likely to take months or years. Border cities like Tijuana could become, in effect, giant waiting rooms for the U.S. immigration system.

Mexico is not prepared to provide housing and other services for what could be thousands of migrants, according to officials and migrant advocates.

“Disaster is the only word that comes to me,” said Pat Murphy, a Catholic priest who runs Casa del Migrante, a large shelter in Tijuana. “We are already living in such a tenuous situation now.”

Officials in other border cities express similar concerns. A major shelter in Ciudad Juárez, also called Casa del Migrante, announced this week that it did not have enough resources to accept any more newcomers. Some federal officials are also worried. After Mexico’s Foreign Ministry announced last week that the country had reluctantly agreed to host the migrants during the U.S. asylum process, the head of the national immigration agency declared it would be impossible to do so in the short term.

“We don’t have the operational structure nor the legal authority for the return” of the asylum seekers to Mexico, Tonatiuh Guillen told reporters.

Homeland Security Secretary Kirstjen Nielsen has said the policy — initially dubbed “Remain in Mexico” — will eventually reduce the number of Central American migrants trying to “game the system” by making unfounded asylum claims. Such applicants often undergo an initial interview and thenmay bereleased from U.S. custody to await a distant court date. Some never show up.

The U.S. government has said the new program could start within days, although it is likely to face legal challenges.

Mexico is already struggling to cope with a 1,000 percent increase in the number of Central Americans who have sought asylum in this country in the past four years. And the government has slashed the budgets for its migration and refugee agencies for 2019 as part of an austerity plan carried out by the new president, Andrés Manuel López Obrador.

“We have nothing, no program, no fund, no support, nothing to receive people who are sent back from the United States,” said María Dolores París Pombo, a sociologist at the Colegio de la Frontera Norte in Tijuana, who specializes in immigration.

The man in charge of dealing with migrants in Tijuana is Cesar Palencia, a city official with an office of five people and a minuscule budget. Until recently, his main concern was the scores of Mexicans being deported each day from the United States.

Most U.S.-bound migrants pass relatively quickly through Tijuana, although there have been occasional crises: In 2016, thousands of Haitians arrived seeking humanitarian protection in the United States. As the U.S. government ended that program, nearly 3,000 of them remained, receiving Mexican work visas and getting jobs.

Most of Tijuana’s two dozen migrant shelters are run by religious groups, and Palencia’s office — created two years ago — can spend only about $4,000 per month for food, blankets and other aid for the facilities, he said.

“It isn’t fair that the U.S. says, ‘I’ll return them [migrants] and you take care of them,’” said Palencia. “The city isn’t ready.”

Tijuana is still struggling to cope with the number of Central Americans who arrived last month in a giant caravan. Around 2,300 are living in pop-up tents in a refugee camp on the eastern side of the city, while nearly 300 more are staying in an unheated warehouse near the U.S. border with no running water, the only light streaming in through a few dirty skylights.

“This could go on for a long time,” Palencia said Monday as he visited the warehouse.

The U.S. government is only accepting a few dozen people a day for preliminary asylum interviews at the Tijuana-San Diego border crossing, and many migrants have not yet signed up for an appointment. Even before the caravan arrived, about 3,000 people in Tijuana were awaiting interviews.

Mexico was so unprepared for the caravan that its members initially were packed into a sports stadium, which degenerated into a muddy, unsanitary mess as rainstorms swept in. In recent weeks, authorities moved the migrants 11 miles away to a former concert venue, which is partially covered. The camp is well-organized with health facilities, regular meals and security, but there are no schools and no day care.

Several migrants interviewed said they had not heard of the new U.S. policy, but that it would not change their plans.

Lesbia Navarro, 36, a weary-eyed single mother, said that after weeks of living with her family in a cramped tent, she had decided to accept a Mexican repatriation offer and would send home her older sons, ages 16 and 13. However, she was determined to stay and seek asylum, along with her 3-year-old son and 12-year-old daughter, to escape the poverty and threats from criminals she faced in Honduras.

“We made it here, and now we want to go to the U.S.,” she said.

In some ways, Tijuana would seem a promising place for migrants to remain while pursuing U.S. asylum. The local economy is humming, with hundreds of assembly plants needing employees, and Mexico has promised to provide migrants with temporary work visas.

Yet, housing is expensive for factory workers who might earn just $240 a month, migrant advocates say. Meanwhile, finding work can take time.

The federal government sponsored a six-week job fair in Tijuana starting last month and encouraged migrants from the caravan to attend. Nearly 4,000 job offers have been extended, said Patricia Campos, who works with the federal employment office — butas of Dec. 24, just 194 people had work. Many, she said, might still be doing the paperwork to get their visas.

Meanwhile, homicides in this city of approximately 1.8 million surpassed 2,200 this year — a record. Earlier this month, two Honduran teenagers who had traveled with the caravan were stabbed and strangled in a robbery in Tijuana, according to press reports.

“We didn’t come all this way to stay here,” said Jonatan Orantes, 27, a moto-taxi driver who said he fled Guatemala because gangs tried to extort money from him. “Mexico isn’t safe.”

Mexican officials have indicated that border communities will not bear an undue burden under the new U.S. policy. The asylum seekers “don’t have to stay in the border area waiting for their immigration appointment,” but can move elsewhere in the country, said Alejandro Celorio, the Foreign Ministry’s deputy legal adviser.

Advocates say the migrants will probably stay near the border, where they can find jobs in manufacturing and keep track of their asylum processes. Exactly how they will manage the logistics of their cases, though, remains unclear.

“They are applying for asylum under U.S. legal standards. How are they going to get assistance from a lawyer in the United States if they are in Mexico?” said Susan J. Cohen, an immigration attorney and president of the board of the Political Asylum/Immigration Representation Project, which helps poor asylum seekers.